Write as a Vector Equality 3a+4b+5z=0 , 6a-10b+5z=0

Problem

3*a+4*b+5*z=0,6*a−10*b+5*z=0

Solution

1. Identify the coefficients of the variables a b and z in each equation to form the component vectors.

2. Group the coefficients of each variable into separate column vectors.

3. Express the system as a linear combination where each variable scales its corresponding vector of coefficients.

4. Set the resulting vector sum equal to the zero vector to complete the vector equality.

Final Answer

a*([3],[6])+b*([4],[−10])+z*([5],[5])=([0],[0])

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